Objectives (5 - 7 minutes)

1. Understand the concept of geometric constructions: The primary objective is for students to understand what geometric constructions are, realizing that it is a systematic and precise method of creating shapes and figures using only tools such as a compass and a ruler.

2. Recognize the main tools of geometric construction: Students should be able to identify and describe the main tools used in geometric constructions, such as the compass, ruler, and square.

3. Perform basic geometric constructions: The next step is for students to actually perform geometric constructions of simple figures, such as triangles, squares, and circles, using the tools correctly.

   • Secondary objective (optional): Encourage students' creativity in performing geometric constructions, allowing them to explore beyond basic shapes and create their own forms.

The teacher must ensure that the Objectives are clearly presented and discussed with the students at the beginning of the class, so that they understand the expectations and can focus on achieving them throughout the activity.

Introduction (10 - 15 minutes)

1. Reviewing previous content: The teacher should start the class by reviewing mathematical concepts that are the basis for understanding geometric constructions, such as the concept of point, line, ray, line segment, angles, among others. This review can be done quickly and interactively, through questions to the students or using visual resources, such as drawings and diagrams.

2. Problem situations: Next, the teacher will present two problem situations that will serve as the basis for the theoretical and practical Development of the class. The situations may be:

   • The first one may be the need to construct a square with a known area, but without knowing the side length.
   • The second one may be the construction of a triangle with internal angles of 30°, 60°, and 90°, but without knowing the side lengths.

3. Contextualization of the subject's importance: The teacher should then explain to the students the importance of geometric constructions, emphasizing that they are used in various areas of knowledge, such as architecture, engineering, art, physics, and astronomy. For example, the construction of the Golden Gate Bridge can be mentioned, which is one of the largest suspension bridges in the world and was designed and built based on precise geometric calculations and constructions.

4. Introduction of the topic: To spark students' interest, the teacher can introduce the topic of geometric constructions by telling a historical curiosity. They can mention that the ancient Egyptians used geometric constructions to demarcate lands after the floods of the Nile, as the waters erased all markings. Additionally, they can mention the famous angle trisection problem, which was one of the great challenges of ancient Greek mathematics and involves constructing a 20° angle, for example.

This Introduction moment should be interactive and engaging, aiming to involve students in the theme of the class and arouse their curiosity and interest in the subject.

Development (20 - 25 minutes)

1. Practical activity #1 - Building an Equilateral Triangle (10 - 12 minutes):

   • Group formation: The teacher should divide the class into groups of up to 5 students and provide each group with a kit containing a compass, a ruler, and a square.
   • Presentation of the challenge: The teacher should present the challenge for each group to construct an equilateral triangle, using only the tools from the kit. The teacher should emphasize that students must justify each step of the construction, explaining how they arrived at the solution.
   • Activity development: The students, in their groups, should start the activity by discussing the best strategy to build the equilateral triangle. They should use the ruler to draw a line segment, and the compass to mark the same measure at two other points on the segment. Then, they should join the points with the ruler, forming the triangle. Finally, they should measure the angles of the triangle with the square to verify if they are equal.
   • Sharing of solutions: After the conclusion of the activity, each group should present their solution to the class, explaining the steps they followed and how they arrived at the construction of the equilateral triangle. The teacher should ask questions to verify if the students understood the concept of an equilateral triangle and the importance of justifying the construction steps.

2. Practical activity #2 - Building a Circle (10 - 12 minutes):

   • Group formation: The teacher should keep the same groups from the previous activity.
   • Presentation of the challenge: The teacher should present the challenge for each group to construct a circle, using only the tools from the kit. Again, students must justify each step of the construction.
   • Activity development: The students, in their groups, should start the activity by discussing the best strategy to build the circle. They should use the compass to draw a circumference on a paper. Finally, they should measure the diameter and radius of the circle with the ruler to verify if they are equal.
   • Sharing of solutions: After the conclusion of the activity, each group should present their solution to the class, explaining the steps they followed and how they arrived at the construction of the circle. The teacher should ask questions to verify if the students understood the concept of a circle and the importance of justifying the construction steps.

The class Development should be guided by the teacher, who should circulate among the groups, assisting students when necessary, asking questions to provoke thinking and reflection, and ensuring that all students are actively participating in the activity. At the end of the activities, the teacher should provide a brief summary, reviewing the main points covered and addressing any possible doubts that may have arisen.

Return (8 - 10 minutes)

1. Group discussion (3 - 4 minutes): The teacher should gather all students and promote a group discussion about the solutions presented by each team. In this discussion, the teacher should highlight the strategies used by each group to solve the proposed challenges, the difficulties encountered, and the conclusions they reached. The goal is for students to learn from each other, understanding different ways to approach the same problem and enriching their repertoire of problemsolving strategies.

2. Connection with theory (2 - 3 minutes): After the group discussion, the teacher should make the connection between the practical activities carried out and the theory presented at the beginning of the class. The teacher should reinforce the concepts of geometric constructions, tools used, and the importance of justifying each step of the construction. Additionally, the teacher should emphasize how practicing geometric constructions helps to consolidate these concepts and develop logical and analytical thinking skills.

3. Individual reflection (2 - 3 minutes): Finally, the teacher should propose that students reflect individually on what they learned in the class. For this, the teacher can ask questions such as:

   1. What was the most important concept you learned today?
   2. What questions have not been answered yet?
   3. How can you apply what you learned today in your daily life or in other subjects? Students should write down their answers and, if they wish, share them with the class. This individual reflection is important for students to internalize what they have learned and realize the relevance of the content for their learning and their lives.

The Return is a fundamental stage of the learning process, as it allows the teacher to assess what students have learned, clarify possible doubts, reinforce the most important concepts, and motivate students for the next classes. Additionally, individual reflection helps students become more autonomous and aware of their own learning process.

Conclusion (5 - 7 minutes)

1. Summary of contents (2 - 3 minutes): The teacher should start the Conclusion of the class by giving a brief summary of the main contents covered. They should review the concepts of geometric constructions, the tools used (compass, ruler, square), and the steps to build geometric figures, such as triangles and circles. Furthermore, the importance of justifying each step of the construction and how it contributes to students' logical and analytical thinking should be reinforced.

2. Theory-practice connection (1 minute): The teacher should emphasize how the class connected theory, practice, and application. It should be reinforced that the theoretical understanding of concepts is fundamental for the practical performance of geometric constructions. Additionally, it should be highlighted that the ability to build geometric figures can be applied in various areas of knowledge and practical life.

3. Complementary materials (1 minute): The teacher should suggest complementary materials for students who wish to deepen their knowledge on the subject. These materials may include math books, explanatory videos online, educational websites, games, and interactive activities, among others. For example, the teacher may suggest that students explore a dynamic geometry software, such as Geogebra, which allows for virtual geometric constructions.

4. Application in daily life (1 - 2 minutes): Finally, the teacher should highlight the relevance of geometric constructions for daily life. It can be mentioned, for example, that the ability to build and analyze geometric figures is important in professions such as architecture, engineering, design, physics, and astronomy. Additionally, it can be emphasized that geometry is present in various aspects of everyday life, such as in art, nature (for example, in crystal shapes and flower structures), in the architecture of cities, among others.

The Conclusion of the class is an important moment to consolidate learning, reinforce the importance of the content, and motivate students for autonomous study. The teacher should ensure that students understand the main concepts, know how to apply them, and feel motivated to continue learning about the subject.